A190149 Even numbers n (written in binary) such that in base-2 lunar arithmetic, the sum of the divisors of n is a number containing a 0 (in binary).

10010, 100010, 100110, 110010, 1000010, 1000100, 1000110, 1001010, 1001110, 1010010, 1100010, 1100110, 1110010, 10000010, 10000100, 10000110, 10001010, 10001100, 10001110, 10010010, 10010110, 10011010, 10011110, 10100010, 10100110, 10110010, 11000010, 11000100, 11000110, 11001010, 11001110, 11010010, 11100010, 11100110, 11110010, 100000010, 100000100

Offset: 1

Author

N. J. A. Sloane, May 05 2011

Keywords

• nonn
• base

Comments

As remarked in A188548, if n is even then most of the time A188548(n) = 111...111 (that is, a number of the form 2^k-1). This sequence lists the exceptions.

Examples

			In base-2 lunar arithmetic, the divisors of 10010 are 1, 10, 1001 and 10010, whose sum is 11011.
		

Links

• D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
• D. Applegate, M. LeBrun, and N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
• Index entries for sequences related to dismal (or lunar) arithmetic

Crossrefs

Cf. A188548, A067399. See A190150 and A190151 for the base-10 representation of these numbers.